Thanks to a rapid progress of high-power lasers soon after the birth of laser by T. H. Maiman in 1960, intense lasers have been developed mainly for studying scientific feasibility of the laser fusion in the world wide. Inertial confinement fusion with intense laser has attracted attention as a new future energy after two oil crises from 1970s -1980s. From the beginning, the most challenging physics is known to be the hydrodynamic instability to realize the spherical implosion to achieve more than 1000 times the solid density. A lot of studies have been carried out theoretically and experimentally on the hydrodynamic instability and resultant turbulent mixing of compressible fluids. During such activities in laboratory, the explosion of supernova SN1987A was observed in the sky on February 23, 1987. The x-ray satellites have revealed that the hydrodynamic instability is a key issue to understand the physics of supernova explosion. After strong interaction of laser plasma researchers and astrophysicists, the laboratory astrophysics with intense lasers has been proposed and promoted around the end of 1990s. The original subject was mainly related to hydrodynamic instabilities. However, after two decades of the laboratory astrophysics research, we can now find a diversity of its research topics. It has been demonstrated that a variety of nonlinear physics of collisionless plasmas can be studied in laser ablation plasmas in the last decade theoretically and experimentally. In the present paper, we shed light on the recent ten topics intensively studied in laboratory experiments. Brief review is given by citing recent papers. Then, modeling cosmic-ray acceleration with lasers is reviewed in a following session as a special topic to be the coming main topics in laboratory astrophysics research.